UQSay #93

The ninety-third UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, January 8, 2026.

2–3 PM — Masha Naslidnyk (Department of Statistical Science, University College London)

Kernel Quantile Embeddings and Associated Probability Metrics

Embedding probability distributions into reproducing kernel Hilbert spaces (RKHS) has enabled powerful non-parametric methods such as the maximum mean discrepancy (MMD), a statistical distance with strong theoretical and computational properties. At its core, the MMD relies on kernel mean embeddings (KMEs) to represent distributions as mean functions in RKHS. However, it remains unclear if the mean function is the only meaningful RKHS representation. Inspired by generalised quantiles, we introduce the notion of kernel quantile embeddings (KQEs), along with a consistent estimator. We then use KQEs to construct a family of distances that: (i) are probability metrics under weaker kernel conditions than MMD; (ii) recover a kernelised form of the sliced Wasserstein distance; and (iii) can be efficiently estimated with near-linear cost. Through hypothesis testing, we show that these distances offer a competitive alternative to MMD and its fast approximations. Our findings demonstrate the value of representing distributions in Hilbert space beyond simple mean functions, paving the way for new avenues of research.

References:

• Kernel Quantile Embeddings and Associated Probability Metrics, ICML 2025

Joint work with Siu Lun Chau (NTU, Singapore) & François-Xavier Briol (UCL) & Krikamol Muandet (CISPA Helmholtz Center for Information Security).

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Vincent Chabridon (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Clément Gauchy (CEA), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Sébastien Petit (LNE), Emmanuel Vazquez (L2S), Xujia Zhu (L2S).

Coordinators: Sidonie Lefebvre (ONERA) & Xujia Zhu (L2S)

Practical details: the seminar will be held online using Microsoft Teams.

If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account).

You will find the link to the seminar on the "General" UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the "fat client", which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

UQSay #92

The ninety-second UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, December 18, 2025.

2–3 PM — Lea Friedli (Engineering Risk Analysis Group, Technical University of Munich)

CRPS-Based Targeted Sequential Design with Application in Chemical Space

Gaussian processes (GPs) have become a widely used tool for modeling unknown functions across various domains. In many applications, particular interest lies in a specific range of the response, with the goal of identifying inputs that lead to desired outputs. To enhance GP model performance in this setting, we employ weighted scoring rules to develop sequential design strategies that selectively augment the training dataset. Specifically, we study pointwise and integral criteria based on the threshold-weighted Continuous Ranked Probability Score (CRPS), using two different weighting measures. We showcase an application in synthetic chemistry, where the objective is to identify molecules with specific properties. However, the presented acquisition strategies are applicable to a wide range of fields and pave the way to further developing sequential design relying on scoring rules.

References:

• CRPS-Based Targeted Sequential Design with Application in Chemical Space, 2025 - github

Joint work with Athénaïs Gautier (ONERA) & Anna Broccard (OFJ) & David Ginsbourger (IMSV, University of Bern).

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Vincent Chabridon (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Clément Gauchy (CEA), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Sébastien Petit (LNE), Emmanuel Vazquez (L2S), Xujia Zhu (L2S).

Coordinators: Sidonie Lefebvre (ONERA) & Xujia Zhu (L2S)

Practical details: the seminar will be held online using Microsoft Teams.

If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account).

You will find the link to the seminar on the "General" UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the "fat client", which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

UQSay #91

The ninety first UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, December 4, 2025.

2–3 PM — Iain Henderson (ISAE-SUPAERO) — [slides]

Multidimensional conformal prediction with random ellipsoids

Conformal prediction (CP) is a popular framework for performing uncertainty quantification on a given a statistical predictor. Its main perks are as follow : (i) little to no assumption on the distribution of the data is required, and (ii) CP provides finite sample coverage garanties. The CP confidence regions are built using a so-called ''conformity score'', which dictates the properties of the said regions. In this talk, I will describe two new conformity scores in a general multivariate regression framework. They are based on a covariance analysis of the residuals and the input points. I will provide theoretical guarantees on the prediction sets, which consist in explicit ellipsoids. We study the asymptotic properties of the ellipsoids, and show that their volume is reduced compared to that of classic balls, under ellipticity assumptions. I will provide numerical illustrations of our results, including heavy-tailed as well as non-elliptical distributions.

References:

• Adaptive inference with random ellipsoids through Conformal Conditional Linear Expectation, 2024

Joint work with Adrien Mazoyer & Fabrice Gamboa (Institut de Mathématiques de Toulouse).

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Vincent Chabridon (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Clément Gauchy (CEA), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Sébastien Petit (LNE), Emmanuel Vazquez (L2S), Xujia Zhu (L2S).

Coordinators: Sidonie Lefebvre (ONERA) & Xujia Zhu (L2S)

Practical details: the seminar will be held online using Microsoft Teams.

If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account).

You will find the link to the seminar on the "General" UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the "fat client", which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

UQSay #90

The ninetieth UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, November 20, 2025.

2–3 PM — Fanny Lehmann (ETH AI Center, ETH Zurich)

Foundation Models of the Earth System: Seeing Beyond Weather

Deep learning has revolutionized weather forecasting over the past three years, with AI models surpassing the accuracy of traditional numerical simulations at a fraction of the computational cost. In this talk, I will present how these models—and specifically, foundation models—can be extended beyond weather forecasting. I will show that the latent space of foundation models is sufficiently rich to predict new physical variables with minimal, lightweight fine-tuning. I will also explore the conditions under which some foundation models remain indefinitely stable for long autoregressive predictions, challenging the common belief that such models inevitably accumulate errors to the point of blow-up. These findings open new perspectives for applying AI models to climate projections and quantify uncertainties in climate change scenarios.

References:

• Finetuning a Weather Foundation Model with Lightweight Decoders for Unseen Physical Processes, 2025

Joint work with the SwissAI Initiative team for Weather and Climate.

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Vincent Chabridon (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Clément Gauchy (CEA), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Sébastien Petit (LNE), Emmanuel Vazquez (L2S), Xujia Zhu (L2S).

Coordinators: Sidonie Lefebvre (ONERA) & Xujia Zhu (L2S)

Practical details: the seminar will be held online using Microsoft Teams.

If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account).

You will find the link to the seminar on the "General" UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the "fat client", which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

UQSay #89

The eighty-ninth UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, October 30, 2025.

2–3 PM — Edgar Jaber (EDF R&D, Centre Borelli, LISN) — [slides]

A Bayesian methodology for hybrid degradation prognostics

Degradation prognostics of industrial assets involves estimating their remaining useful life (RUL) by projecting current health indicators and operating conditions while quantifying associated uncertainties. These prognostics are central to the development and deployment of digital twins, which aim to provide insights into the evolving state of complex systems. Traditionally, RUL estimation relies on physics-based simulations or data-driven models. While both have their merits, they can prove inadequate when simulation runtimes are prohibitive or when degradation data is sparse, common challenges in digital twin implementations for critical industrial infrastructure.

To address this problem, we developed an offline modular data assimilation approach. Firstly, a Bayesian model updating strategy combines kernel-based sensitivity analysis to identify and rank the time-varying influence of the model’s input variables, with a tailored inference scheme that accounts for the heterogeneity of available data. Posterior distributions are sampled using MCMC techniques, while the method mitigates the curse of dimensionality by iteratively updating the marginals of influential input variables under an independence assumption. Posterior informativeness is quantified through the Kullback–Leibler divergence, comparing updated distributions to their priors. Secondly, the full state distribution is updated with the help of an ensemble Kalman smoothing step, further reducing the posterior uncertainty.

After detailing the methodology, I will illustrate how this approach enhances the fidelity of RUL predictions and reduces uncertainty in a clogging prognostics use case for digital twins of steam generators in nuclear power plants.

References:

• Fusion of heterogeneous data for robust degradation prognostics, 2025 - github

Joint work with Emmanuel Remy (EDF R&D) & Vincent Chabridon (EDF R&D) & Mathilde Mougeot (ENS Paris-Saclay) & Didier Lucor (LISN).

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Vincent Chabridon (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Clément Gauchy (CEA), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Sébastien Petit (LNE), Emmanuel Vazquez (L2S), Xujia Zhu (L2S).

Coordinators: Sidonie Lefebvre (ONERA) & Xujia Zhu (L2S)

Practical details: the seminar will be held online using Microsoft Teams.

If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account).

You will find the link to the seminar on the "General" UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the "fat client", which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

UQSay #88

The eighty-eighth UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, October 16, 2025.

2–3 PM — Virginie Ehrlacher (CERMICS, Ecole Nationale des Ponts et Chaussées) — [slides]

Marginal-constrained modified Wasserstein barycenters for Gaussian distributions and Gaussian mixtures

The aim of this talk is to present some modified Wasserstein barycenters for probability measures defined on cartesian product sets which satisfy given marginal constraints. We focus on the specific case of Gaussian and Gaussian mixture distributions, as the proposed approach strongly relies on new results about properties of geometric means of covariance matrices. In the case of Gaussian distributions, the marginal-constrained modified Wasserstein barycenters can be analytically computed, while for Gaussian mixtures, computing the marginal-constrained barycenter consists in a postprocessing of the Gaussian mixture Wasserstein barycenter. In both cases, we provide numerical simulations illustrating the difference between Wasserstein barycenters and modified marginal-constrained Wasserstein barycenters. We moreover provide several test cases where the marginal-constrained Wasserstein barycenters interpolate better than regular Wasserstein barycenters, showcasing the practical interest of the proposed approach. As a by-product, we prove new results concerning marginal-preserving Wasserstein barycenters. Indeed, Wasserstein barycenters do not preserve marginals in general. In this work, as a consequence of the derived properties on the geometric mean of covariance matrices, we obtain sufficient and necessary conditions for the Wasserstein barycenter between two Gaussian distributions to preserve marginals, and provide necessary conditions in the case of more than two Gaussians.

References:

• Marginal-constrained modified Wasserstein barycenters for Gaussian distributions and Gaussian mixtures, 2025

Joint work with Maxime Daléry (LMB - Université Franche-Comté) & Geneviève Dusson (LMB - Université Franche-Comté).

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Vincent Chabridon (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Clément Gauchy (CEA), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Sébastien Petit (LNE), Emmanuel Vazquez (L2S), Xujia Zhu (L2S).

Coordinators: Sidonie Lefebvre (ONERA) & Xujia Zhu (L2S)

Practical details: the seminar will be held online using Microsoft Teams.

If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account).

You will find the link to the seminar on the "General" UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the "fat client", which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

UQSay #87

The eighty-seventh UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, September 18, 2025.

2–3 PM — Pamphile Roy (LUT Business School, LUT University - Consulting Manao GmbH, Austria) — [slides]

A novel way of visualizing causal uncertainty

Global sensitivity analysis (GSA) is crucial for understanding model behavior and informing decision-making. However, its adoption is hindered by methodological complexity, implementation challenges, and high computational costs. To address these issues, we developed Simulation Decomposition (SimDec), a hybrid approach that simplifies GSA through efficient computation of variance-based sensitivity indices and intelligent visualization techniques. SimDec is made accessible to practitioners of any background via a no-code web dashboard. The latest enhancement to the SimDec dashboard includes two-output graphs, which allow users to visualize relationships between two model outputs alongside their marginal distributions. This feature is demonstrated through a case study on optimizing a heat exchanger in a nuclear reactor, examining the relationship between the levelized cost of heat and mechanical design characteristics. By providing an intuitive, no-code interface, SimDec democratizes GSA, making it accessible to users with limited mathematical training. This work was presented at the SAMO 2025 conference, highlighting the potential of SimDec to transform how sensitivity analysis is conducted across various fields.

References:

• Uncovering heterogeneous effects in computational models for sustainable decision-making, Environmental Modelling & Software 2024
• Simulation Decomposition in Python, Journal of Open Source Software 2024 - [SimDec dashboard]
• Simple binning algorithm and SimDec visualization for comprehensive sensitivity analysis of complex computational models, Journal of Environmental Informatics Letters 2025

Joint work with Mariia Kozlova (LUT University) & Andrea Saltelli (UPF Barcelona School of Management) & Julian Scott Yeomans (York University).

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Vincent Chabridon (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Clément Gauchy (CEA), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Sébastien Petit (LNE), Emmanuel Vazquez (L2S), Xujia Zhu (L2S).

Coordinators: Sidonie Lefebvre (ONERA) & Xujia Zhu (L2S)

Practical details: the seminar will be held online using Microsoft Teams.

If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account).

You will find the link to the seminar on the "General" UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the "fat client", which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.